Syllabus - Biostatistics (BM702 (B))

Data Collection and Sampling Methods

Concepts of population and sample and need for sampling methods of collecting data. Types of sampling- simple random sampling with and without replacement, errors in sampling and data acquisition. Statistical tests of hypotheses, box plots of a data sample, distribution & scatter plots.

Random Variables

Discrete and continuous variables, probability mass function, probability density function and cumulative distribution function, jointly distributed random variables: marginal and conditional distributions, independence of random variables. Expectation of a random variable and its properties, expectation of sum of random variables, product of independent random variables, conditional expectation and related problems, moments, moment generating function & their properties, random vectors and central limit theorem.

Distributions of Function of Random Variables

Distribution of sum, product and quotient of two variables, reproductive property of standard distributions, χ2 (chi-square), t and F distributions (central cases only) and their limiting forms, bivariate normal distribution and its properties, tests of goodness of fit, tests of independence.

Statistical Filtering Process

Adaptive filtering: principle and application, steepest descent algorithm convergence characteristics, LMS algorithm, convergence, excess mean square error, application of adaptive filters, RLS algorithm, derivation, matrix inversion, initialization. Finite time estimation of mean value, correlation, synchronous averaging, regression, multiple and partial correlation, one-way and two-way analysis of variance (ANOVA).

Case Studies For Biomedical Application

Processing of biomedical signals like ECG, EMG, EEG etc., removal of high frequency noise (power line interference), motion artifacts (low frequency) and power line interference in ECG, cancellation of ECG from EMG signal. Introduction to principal component analysis (PCA), Covariance matrix, residuals from PCA, PCA estimations from raw data matrix.